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Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
book

Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition

by Andrei D. Polyanin, Vladimir E. Nazaikinskii
December 2015
Intermediate to advanced content levelIntermediate to advanced
1643 pages
59h 33m
English
Chapman and Hall/CRC
Content preview from Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
688 SECOND-ORDER HYPERBOLIC EQUATIONS WITH TWO SPACE VARIABLES
Here,
G(r, ϕ, ξ, η, t) = exp
1
2
kt
X
n=0
X
m=1
A
nm
J
s
n
(µ
nm
r)J
s
n
(µ
nm
ξ) cos(s
n
ϕ) cos(s
n
η) sin
λ
nm
t
,
s
n
=
ϕ
0
, A
nm
=
4µ
2
nm
ϕ
0
(µ
2
nm
R
2
+ β
2
R
2
s
2
n
)
J
s
n
(µ
nm
R)
2
λ
nm
, λ
nm
=
q
a
2
µ
2
nm
+ b
1
4
k
2
,
where the J
s
n
(r) are Bessel functions and the µ
nm
are positive roots of the transcendental
equation
µJ
s
n
(µR) + βJ
s
n
(µR) = 0.
7.4.3 A xisymmetric Problems
In the axisymmetric case, a nonhomogeneous telegraph equation in the cylindrical coordi-
nate system has the form
2
w
∂t
2
+ k
∂w
∂t
= a
2
2
w
∂r
2
+
1
r
∂w
∂r
+
2
w
∂z
2
bw + Φ(r, z, t), r =
p
x
2
+ y
2
.
In the solutions of the problems considered below, the modified Green’s function
G(r,
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Publisher Resources

ISBN: 9781466581494